COMPUJTER P1RO04HA-~ BAT

COMPUTES AN~D M~AWS

E=~T OPERATING OHRACTR&CS1TIC CUMV

TfffPMGWO4~ICT PROBADILIT'Y DIST1'R-hU!IO4

DONALD C. RAPPAPORT'

*NOVEMBR 19711

TECHNICAL SUPPORT DIRECTORATEPICATINIIY ARSINAL

[it~~v d for public rolesa.; distrilxatia2 uulmited.

411

THIS DOCUMENT IS BEST

QUALITY AVAILABLE. THE COPY0

FURNISHED TO DTIC CONTAINED

A SIGNIFICANT NUMBER OF

PAGES WHICH DO NOT

REPRODUCE LEGIBLY.

Sled" Cam~mingm00C~UMT CONTUL DATA.- R & D

g~w aga.uhsa M.1 a" * of a","# 6.0.6adamUm Raw~ 60 d asmi. Bhm atue owma a Is ta~1. Of@ReMATweLTS IYB fumpsf awn"r 0a.sPORT 9CURITY CL*WIUPCA ONu

S.AOTTITLEMA COWUTU PROAX THAT CMIhPUS AND 3AWS

Mi REACT OPUNlM CHARACTI3STV CUII US3N0 TH3MPUU WWRIC PROBABILITY D33223339TION

S.AUTbWRMI (P~ms urnS M-W am *W)

Demald C. Reppqpart

REPORT GAVE 10. TDTA& "O. or pas" 11. RO. OU 09"~

iovewea IM7 24 r 2GL. CONTRACT ON GRANT NO.Lm OUN-OIATON' REPORT mUýEAN

b- PRGJCT NO.Teca iclAl RePort 49

GL W*. PerT NOIW (Aw 01wminm MBel he aps .t.

AI I. SUPPILMAUNTARY MOTES2 10e01600000 SLITARY ACTIVITY

fteatimy Amms~lIU.S. Arar *Itions Comamnd

IS.TA~ computer progra was developed whift uns. the HyperpamtriO Praobbilit~y

DietributlaD In Iotq n plott"n de~tfective vs. 10 Imartuit probsbilityof acoviptZ3@ points, (.9, 0975s 0959 .90# o75# .50# .25, .109 .05 and .01).

Do xo"173=uS.=2

X~ ~ mywms1MXA1M M

ftot (%watiu Cbwactuistin OCwv

24. WCLASWUDI-

TAMAZ OF CONTMTS

*?S~clc.PageSMIARY 1DISCUSS1EN 3

FCBTRAN PEOAN

A. ]rput, 13B. Sample Output1

TABL OF DISTRIBUT2DK 19

ABSTRACT DiTA 23

Ww

A 6iaterprop iwelqmd *Soh Noa I~ -,go=r1PkobWlf#Distibutn I oa~utbg ami oottft petaint isfootftlvu.

10 Sqisbanat probab111P7 of asooptno. puipts (.999 09"s~ *95 *90# 075o.%09 0250 010 0 005 ald .01).

21

An operating l beracteristic curve ina £tool used In quality cotrolfor ti pmupose of buing or selling .mmfactured pods.

Using the formulas and olution an discussed In Reference 1 anda2it, rIg th I(IM* computwr program described In that Reference, a newpogrm wase generated tLich computes and plots percent defective for 10important probability of acceptance levels. Additional related informa-tion printed out lot defeotives in original population, re3iability,aed aonfidence level.

rotes Since it In quite wmusua1 that a sample will exceed 50% ofthe popualaim this condition bis not boen programed. If it Js desiredto compute this, use the equalities as shw.n and discussed an page I ofReference 2.

AV44-AF

- , . . . . .. . ... ... -i i - i [ -

Forlm m'm

DIMENSION 04601.BOPU 160),PAC(601.PACL(60).SOPL(60),PACCTI1O),

DATA PACCTIf.99,.9?5,.959.9O..15,.5,.2S,.1@,O$.01/.lWKIrL (bfWrilICAkLL jPLjo! 1*;3*-31

200 FORMATWIFO0)0

10243 IF (SAMPLE - OEF)S6Q,560.563

SO O5 i 61a /,ZA'N PROBANILITY OF OBTAINING *vF10.@,' UEFEM'S~ OR MaI A" 35Lt~ OP-9r&U.U.. AD9*dVAO*UAT3 I KLUA14UCLZZ0F THlE NUMNER Of INTERESTING ONES IN THE POPULATION-*)

S03 IF tSAMPLE - POID/2.156S5*S65b64

1 ; ORMAiT (I1.20(/),7:20:.*NFOW YOU HAVE DONE IT, I TOLU YOU NOT TO EN_lTLK - 54"PtL 319 WK&fKf9 R gFlRM ire UP FRlE rVIUL4Agrlm rvui 9

20 INTERED A SAM4PLE SIZE aP.,F1oo:.0 ANWRIOlit A POPULATION SIZE Of*#arueel' pU~gavtlP vuu LA9%. .1110 V"V§fNfN ran MAIL WILL Ot ACL"tlU.*4)

20 ORMAT f(III1,/SOA.30HOPEMATING CHARACTERISTIC CURVE#

2F9,09SX91SMACCEPTABLE DEFECTSFo.0,/126MMIF DEFECIIVESol1.7HPERC4CM1I gA~l SSvlMNUA9&Ll IT ,r9AqA,*fILLlAAMALjlTqgOxq4I0MOHCFIIoENCEf.2?tI~lmlW OaZntaAL.7A,9HOEFECTIVEthA.IOMACCEPTANCE#

30 bI0E.2HIS9I3X9ZIIISI//

475 CONF w PACC~TICON)

IF (AREA - .699 1477,476,4745(9 SUL33*IUNE - 4. 17 ZOALL I - rUP

IF IGUESS - POP - SAMPLE) 2600,26126190! GU wF- - lo 0 ULF - SIMLE

260 CALL BACK (POPSAMPLEGUESSDEF.RELCTMERS.ASUN.BAC.POPO)

40 HOPO(l) a POPOUOLbb wlUEPSC.If3FW'LLJ 9 POP

CALL UACIC (POPSAMPLEGUESSOEFRELOTMERSAsSUNBeAC.POPOI

UOPOM2 4 POPD ___________________

AT ( "uplulal - 5~uruseIl (Trg F(S.!7U

779 (iUESS a PUPO - 4.GALL BACK PPAML9UO*~',LIIN.,UAUUU

PACII) a SACno~urill - rgur

so0?778 DO070? 1.03920

0111 * GOP0 (1-2) - (.S - PACII-2) -AREAl/ PAC(III * PACIZ-2)&1 0 iMWupuAEI - ouQPulAAIIIF 1(j() - DEF) 4019402#402UUL' o ULF' a .

0022 ..s aol%03'~T C1166 MU

6bl JEST a 4II

all *(I) IOPI -9001-Ig- .11.?l,b-swamN -.

PAC IF ) A aE 4 *.PC(41)g,0.

Sb ~~~JESTu a_ _ __ _ _ ___I_ _ _

(I Iu* appPg4*g

tog CONgINK iI1

.v-1 I-vw . .-@ .

50TO pug01 GUES *011)I -9 POP) 21@4S9IL,1 0 PO

-v -I - s1 3609360036Up GESS a LF

N*K 1 af tf91U' O

- at GUESS a * K 1 SML O

if@ Abd 509 SWISS 19 SMLE11 O * PSi0

3" gu P ISur rw W -O . -4,__ _ _ _

wo 00? 1 -_ _ _ _ _ _ __W__move_

fit GUS U( SP* .#aN9Irwt it*PO

1111110 '"M CDC "maa*9ieV9*0 -- -- - e m s

191 4951 a II

IF CUS IUOPL(II - COPLIS-111 30Il31119.M*11

Ift 320N Ip" cWIMIM-1e - AM1*IN?,N?.0316so, DO *3w A - move

J95T at

320 Silo a oil-it-S 1.

130 ~ w RIIIJ

AST 8Cl, 104

-IMU - W. a

'am 1111 - IWO.________009 100. I) *PO

Pots a NCAST-a

SeC 1004. I. a POPS

Ma0 TOc TO94SO

~P 12; 110- . I I,- PA=

16009 a 003.51 -CI U)DA 0W

paI a PA"eITU

PO0L

I,, 40 FORMAT il$

IF Sle" 1 67I 9ThO 64.S4ZVO p9 &;Au - -

-. CALL lUIL 1pSoiUU.1se.lsteel$,IS..I

"is..eea.sew Well @of 0 346400a..CM 5* UUY~I L XX UP .UwvTu1i WIU U

COL f16 t yel .We WSUe 95

"CU, ft53*.0 ______

00u TO 4

4" VoUIN 110191917-f~epomU' U101ma Wl WIPIN15 SWIq £~~SINJ FOR M~. ISTA .O ______ ______- - - - -

RW VOIAN egW4UoM 9)tommelle..u.."I STOP

- -- --- - ---UT ----

103 if tPOP - POPO)IIb6i*ii _____________

POPO IGLOO

130 GLesO * POP . SANPLE * SEP .1

. - -a

IF (POPS -POP/2a11us9iig0ai1

T a &AMPLE

o.ini I i. I . ti -OTHERS a POP - POPS ____X - 1009 - HV6

toSs 1un. - SAC

0i W SAMPLE - W0 .______

T a SAMPLE

* SUNM AMM9 IZOY.A.W)

- .- *30 OTH90S *POP -POPS ________

"RETURN

90 la ASF

11 ong a 01ANK 1.1

G0PO -1 etv-is LENNY 0

SYDELL * W1LARY - BRANl

ROWC SVSILL - MAYfr 1.1.2000 s# 555

-x --- w-u $vvet r--_ _ __ _ _ _ _ _ __ _ _ _ _ _

as TOOT00 a KLMLAI3 afts *V - V 9

HE"S a too ________________________________

- - 17 ( jYut. 21#6604u.as CONTINUE_____________ _____

aS- 1133U' W*.UW OI fFXv I NI~EW S

TooY a TORY - 1.-6.tf HICIPV w

JOYCE a JOYCE * I00 .0 to

is 4 CONTaINUE____ _______________

IF ("E *f S **.St ~ tv W~l SP -

IF ill - LENNY) 83939-- 8- c~m cvv--wnr-------- -- -- _______**- ---

'Ems "111141 ALOGSI f(MAY.OIAUZIEERWAN I*)1* CLAMA))

AS K~~~NMC U NAUC * . _____________

up..u - wspeu -RAY * MAY -1.__________ ______

13 ANNlE F LOmv* -91%1-.O

- a '.~ ~ -- _--------------------_ _ _

mzS

1. Donald C. Rq~p~rts A omter PEO for Exact Re liability and

PicatinnyAsea Tbbuioa1 eprt U1, Jamwy 19f.

2. G.J. Liabom anmdD. B. Oven# Tajso h trio

ZtbiIDxrbggSatod.Uiest rsSafrs

call-ralap1961

APPSIOZ A

CAM ~ -vw tozMat

1-10 POPVU#AtOO r 10.0

1.1-20 8sqwle F 10.0

21-3D Dseeoti,.s F 10.0

13

APPENDIX B

s a output

')PERIAIING C04ARAC~T.L4ST1C CURVE

POP piLA!1Urv h~ So* SAMPLE. 100 ACCEPTAuLFr I*FCTS 1.

IF ULFEC11Ik) PE.RCENI PHMOAIAHL1TY Of RELIAOILITY CoNFluEwCE

TN U.4IGINAL "O.FECTIVE. ACCEPIANCE. is is

PO0PJLArIuN AWL is is

1. 700 10000000 96.00 .000000

4.00 0963265 96.00 .006735

1.0 1000~o0000 96000 0000000

4.00 096326S 90.00 .03b7l6

4.00 .963206 90.00 *OJ6736

3. 6000 .902061 94.00 90979S9

3. 6.00 *90d041 904.00 .097q95

40 .*0 oR2563e 91.00 .174164

*4. 8*00 .425636 912.00 .171,41

5.10.00 .741900 90.00 .256100

To 14.00 OS70934 86.00 0429066

8. 6*00 0*90502 84.00 .509498

Its 22.00 .286617 78.00 .711183

12. 24000 .236449 76.00 .7b3551

IS. 30.00 .12097S 70.00 us7902#5

16. 32,00 .094463 68000 .905537

1036 16.00 .056430 66.00 094457U

14. ARO00 o04160? 62.00 0956393

P3. 46.00 .011315 54.00 .986005

240 44.00 0007617 92.00 .992163

4

J4!4

H+f-

1 H 1 R4R;

t 1 H! 11-144M . V,

M iý

jT1144-4a -

Zft-Fql;lý"i

I Alfff

ILI-

-Ti

#tau

SOPERATING CHARACTERISTIC CURVE

POPULATION SIZE 12345o SAMPLE 4560 ACCEPTABLE DEFECTS .13

S IF OEF9CTIVE§ PERCENT PROBABILITY OF NE.,IABILITY CONFIrENCEIN ORIGINAL DEFECTIVE ACCEPTANCE IS IS

POPULATION ARE IS IS

169. 1.3T 0990082 96.03 00099161700 1.38 .989609 96.02 o010391

1910 lss5- 97S010 98645 902490192* 1.*S6 974018 98044 .025942

211. 1071 .950526 96.39 .049472* 212. 1.72 0946980 96.28 .o81020

236. 1.91 .901517 98.09 o09448323?. 1092 0699096 98.06 .100904

2•63 2.29 *751692 97.71 .246306284. 2.30 0747611 97.70 .252189

342. 2.7? %S01663 97.23 .496317343o 2.76 9497393 97.22 .502007

4060 3.30 .252613 96070 07471474090 3.31 .249799 9.069 0750101

475 3.89 .100760 96o1S .699640476. 3086 .099233 96014 .900767

S116 4.20 .050349 95.60 0949601S190 4.20 0049500 91.60 *"0$s00

60s0 4.90 .010041 99.10 0.999596060 4091 .009842 9"009 .990116

S"16

tNOT. REPRODU0

1 ;4 4